1. Technical Field
A “Rational Z-Buffer” provides techniques for reducing artifacts when rendering graphics using z-buffers, and in particular, various techniques for reducing the likelihood of z-buffer collisions when using hardware or software z-buffer algorithms to render graphics.
2. Related Art
As is well known to those skilled in the art, the z-buffer algorithm is the most common technique for displaying only the visible portions of a scene in 3D computer graphics applications. It is generally implemented in graphics hardware, though software-only implementations can be used as well. The term z-buffer refers to an array of numbers whose dimensions correspond to the pixel array of an image, or frame-buffer, to be rendered. The computer representation of these numbers varies; they are typically 16- or 32-bit integer or floating point, but can be any size desired, depending upon the available graphics hardware or software.
The imaging model used in typical 3D computer graphics can be thought of as a collection of rays passing from an eye-point through each pixel in an image-plane. The distance from the eye-point along such a pixel ray is the associated depth, or “z value” of the pixel. All values of the z-buffer are initialized to be greater than the largest expected depth value in a scene. Geometric primitives such as, but not limited to, triangles and line segments, are rasterized by determining which pixels of the frame buffer they cover, and at what depth.
The z-buffer algorithm works by performing a z-test on every possibly visible pixel in a scene. The z-test works as follows: before writing the color value associated with a primitive at a pixel, the (new) z value of the pixel is compared to the (old) z value associated with the pixel stored in the z-buffer. If the new z value is less than the old z value, then the color is written to the frame buffer and the new z value is written to the z-buffer. After all primitives are rendered, only portions of primitives closest to the eye-point will be visible. This corresponds to physical reality where close object occlude distance ones on the same line-of-sight.
Unfortunately, one of the problems with the use of conventional z-buffer algorithms is that since z-buffers represent numbers with finite precision, it is often the case that distinct depth values for different pixels map to the same values when rendering images using z-buffers. This type of z-buffer collision often causes visible artifacts in images at the level of individual pixels.